Growing popularity of multimedia applications, pervasive connectivity, higher bandwidth, and euphoric technology penetration among bulk of the human race that happens to be cellular technology users, has fueled the adaptation to Long Term Evolution (LTE)/ System Architecture Evolution (SAE). The LTE fulfills the resource demands of the next generation applications for now. We identify security issues in authentication mechanism used in LTE that without countermeasures might give super user rights to unauthorized users. The LTE uses static LTE Key (LTE-K) to derive the entire key hierarchy, i.e., LTE follows Evolved Packet System Authentication and Key Agreement (EPS-AKA) based authentication, which discloses user identity, location, and other Personally Identifiable Information (PII). To counter this, we propose a public key cryptosystem named, 'International mobile subscriber identity Protected console Grid based Authentication and Key Agreement (IPG-AKA) protocol' to address the vulnerabilities related to weak key management. From the data obtained from threat modeling and simulation results, we claim that the IPG-AKA scheme not only improves security of authentication procedures, it also shows improvements in authentication loads and reduction in key generation time. The empirical results and qualitative analysis presented in this paper proves that IPG-AKA improves security in authentication procedure and performance in the LTE.